How can I get rid of this bulge?
You should have added that picture; I'll bet a hundred would know in a second. It's the inside of the glove poking the wrong way. It's weight is too strong and possibly to the wrong bone. It's outpacing the outside of the glove (assuming it's a glove specifically) and moving faster than the positive-facing normals. That gray strange color is the dead giveaway; those normals are flipped and display like that when you haven't enabled 2-sided. (I'm glad you didn't enable 2-sided or it wouldn't show up so clearly.)

Less weight will reduce your swelling. That will keep the gap between outside and inside from inverting. Depending on your needs, you might paint that portion to another bone? I understand the problem but can't tell you the perfect solution for you.